Four diamond films were deposited by the microwave plasma assisted chemical vapor deposition method varying CH4 concentration from 2.5 to 10% in the feeding gases. Thermal conductivity was measured on these free standing films by the steady state method from 80 K to 400K. They showed higher thermal conductivity as the film deposited with lower methane concentration. One exception, 7.79% methane concentration deposited film, was observed to be the highest thermal conductivity. Phonon scattering processes were considered to analyze the thermal conductivity with the full Callaway model. The grain size and the concentration of the extended and the point defects were used as the fitting parameters. Microstructure of diamond films was investigated with the scanning electron microscopy and Raman spectroscopy.